Pith Number

pith:GTAILDP3

pith:2001:GTAILDP3NZIXZPIDZHPKK7PRDV

not attested not anchored not stored refs pending

Linear perturbations in a universe with a cosmological constant

Antonio Vale, Jose' P. S. Lemos

arxiv:astro-ph/0101500 v2 · 2001-01-28 · astro-ph · gr-qc

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GTAILDP3NZIXZPIDZHPKK7PRDV}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-07-04T15:20:39.264007Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

34c0858dfb6e517cbd03c9dea57df11d59958bf723a434e070225bd972c602e4

Aliases

arxiv: astro-ph/0101500 · arxiv_version: astro-ph/0101500v2 · doi: 10.48550/arxiv.astro-ph/0101500 · pith_short_12: GTAILDP3NZIX · pith_short_16: GTAILDP3NZIXZPID · pith_short_8: GTAILDP3

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/GTAILDP3NZIXZPIDZHPKK7PRDV \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 34c0858dfb6e517cbd03c9dea57df11d59958bf723a434e070225bd972c602e4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "64ec549d72aff3ff5c820ebde843aed929041f9738ef4060026900669bbf333f",
    "cross_cats_sorted": [
      "gr-qc"
    ],
    "license": "",
    "primary_cat": "astro-ph",
    "submitted_at": "2001-01-28T17:52:55Z",
    "title_canon_sha256": "487d7d7d537459e64f97366d59ca7d0dd676a0f7aa4c26da4fc0a138fa7f24fb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "astro-ph/0101500",
    "kind": "arxiv",
    "version": 2
  }
}